According to a new round of NBC-Marist polls, President Barack Obama holds narrow leads over Mitt Romney in three important battleground states.

In Ohio, Obama leads Romney 48 percent to 42 percent. In Florida and Virginia, Obama leads by identical 48 to 44 percent margins. All three polls have a margin of error of plus or minus 3 percentage points.

Obama’s chances are helped by a belief that the economy is rebounding, as majorities in all three states believe that the worst of the economic downturn has passed. Furthermore, although Romney holds a narrow lead among men in all three states, Obama is routing him among women. In Florida and Virginia Obama leads by 10 percent among women, and in Ohio Obama leads by 12 percent.

While Obama’s leads are slim, the numbers suggest that they have room to grow. In both Virginia and Ohio, 58 percent of voters who strongly support their candidate favor Obama, compared to just 42 percent for Romney. Obama also leads among such voters 55 to 45 percent in Florida, suggesting that the president may be able to swing some current Romney supporters to his side.

As MSNBC’s First Readpoints out, these three states are especially critical for Romney:

All Obama has to do is win ONE of these, and he’ll likely surpass 270 electoral votes. Yet even if Romney wins all THREE, Obama still has a viable, though, slim path to 270 (if he wins Colorado, New Mexico, Nevada, Iowa, and New Hampshire). But make no mistake: Romney most likely needs to win all three states, while Obama’s goal is to win two — or maybe even one. Why is this the case? It’s the president’s advantage in the West right now. If Romney can’t pull at least Nevada, it puts a TON of pressure on him to sweep these three battlegrounds.

So unless Romney is able to attract enough Latino support to compete in the West — which seems unlikely given his “severely conservative” policies and the antics of his party — he will need to turn his numbers around in these states to have any chance of winning the White House.